GYanggg

Hello Guest!

This is an equation of a line.

We can rewrite it in point-slope form:

-2x = -1 - y

2x=1+y

y=2x-1

We can then graph this line by plugging in 2 points then connecting the two points. 

Two points that work are:

(0, -1) and (2, 3) 

You can then connect those two points on a graph and all the points on the line are solutions. 

I hope this helped,

Gavin

Point-Slope form is:

y - b = m(x - a)

Where m is the slope, and (a,b) is a point the line passes through. 

Since we are already given the points, we can plug them in to update our equation:

y - 7 = m(x - (-5)) 

Simplyfied:

y - 7 = m(x + 5) 

We now need to solve for the slope. 

The slope is rise over run. 

Rise is the first y value minus the second y value. 

Run is the first x value minus the second x value

Rise is 7 - 0 = 7 

Run is -5 - ( -4 ) = -1 

The slope is -7. 

The equation in point-slope form is y - 7 = -7(x + 5) 

Yes, I realized my mistake, 

It was a careless one again. :)

Hi Guest!

There is a rule about 30-60-90 triangles. 

As shown by the image, each of the sides of the triangle has a relationship. 

So if the length of the hypotenuse is \(2\sqrt6\), we can write an equation to solve for the legs. 

We call the legs x and √3x 

Using the pythagorean theorem, we get:

\(x^2+(\sqrt3x)^2=(​2\sqrt6)^2\\ x^2+3x^2=2\cdot6\\ \)

You can solve for x, then plug in x to find the value of the two legs.

You then add the values to find your answer!

I hope this helped,

Gavin

10.

Following the diagram, there is a theorem that states:

AX * BX = DX * EX

You can use that to solve for x. 

\((x+10)(x+1)=x(x+13)\\ x^2+11x+10=x^2+13x\\ 2x=10\\ x=5\)

I am not going to answer 5 and 9, but just tell you how to do it. 

You use that formula to solve for x and find pq. Good luck!

I hope this helped,

Gavin

The method I used was over complicated and easy to mess up. 

Simply view GingerAle’s post for the correct method and answer. 

Sorry for the inconvenience,

Gavin

\(\sqrt{1000} = \sqrt{100\cdot10} = \sqrt{100}\cdot\sqrt{10} = 10\sqrt{10}.\)

It's irrational since √10 is irrational since there exists NO integer which, when squared, = 10.

Yes it is rational. 

This is because it can be expressed as a fraction 3.10723 is also 3 10723/100000

note: not all decimals are rational, pi is an example of an irrational decimal.

\((\frac{1}{3})^4=\frac{1^4}{3^4}=\frac1{81}\) 

I hope this helped,

Gavin

This is a simple choosing problem. 

15 choose 2 can be expressed as:

\(\binom{15}{2}=\frac{15\cdot14}{2\cdot1}=105\)

i hope this helped,

Gavin